Matchings in random regular bipartite digraphs

Abstract

Let G be a random directed bipartite graph with n nodes in each class and outward degree d at each node. The probability G contains a matching is shown to approach one for large n if d≥2, but to approach zero if d=1. This result contrasts with a result of Erdös and Rényi which implies the probability of a matching goes to zero if the number of arcs (chosen at random without regard to regularity) grows more slowly than n log n. © 1980.